I bought the '99 Odyssey in 2006. So far it's been good to us. This was not subject to a transmission recall. Knocking on wood.
Five-star crash rating, especially side impact. Didn't want a minivan but decided it was safest way to go for our kids. I hated it at first but now like it. I feel pretty safe in it, and it's good for hauling things as we fix up our house. (Middle-row seats can be removed from car.)
I'm sure Honda has improved this already, but the automatic doors are very slow (especially annoying when you forgot something inside and have to wait for it to close then wait for it to open), and the one on driver's side always sticks. No button to open rear/hatch door. Speakers only in front.
† Edmunds.com received the highest numerical score in the proprietary J.D. Power 2014 Third-Party Automotive Website Evaluation Study℠. Results based on responses from 3,381 responses, measuring 14 companies and measures third-party automotive website usefulness among new and used vehicle shoppers. Proprietary study results are based on experiences and perceptions of owners surveyed from January 2014. Your experiences may vary. Visit jdpower.com.